That’s the cautionary message that emerges from the latest Associated Press Economy Survey.

Europe’s recession will persist deep into the next presidential term, according to a majority of the 31 economists who responded to the survey. A weaker European economy would shrink demand for U.S. exports and cost U.S. jobs. Yet there’s little the next president can do about it.

An even more urgent threat to the U.S. economy, the economists say, is Congress’ failure so far to reach a deal to prevent tax increases and spending cuts from taking effect next year — and possibly triggering another recession. Yet as President Barack Obama has found, the White House can’t force a congressional accord.

And whether Obama or his Republican challenger Mitt Romney wins Nov. 6, he’ll likely have to deal with one chamber of Congress led by the opposing party. Polls suggest the Senate will remain in Democratic hands after the election and the House in Republican control.

“It’s not like there’s a clean slate for someone to do what they want,” says Joshua Shapiro, chief economist at MFR Inc.

Still, there are some ways in which the economists think the White House will be able to drive the economy.

The next president, for example, could help lift growth and reduce unemployment by backing lower individual and corporate taxes and looser business rules, more than 70 percent of the economists say. They think such policies — the core of Romney’s economic message — would be more likely to help than would Obama’s plans for more spending on public works and targeted tax breaks for businesses.

Only about one in five of the economists say Obama’s policies would be more likely to help spur growth and reduce unemployment.

The economists were surveyed before the government estimated Friday that the economy grew at an annual rate of 2 percent in the July-September quarter — too slowly to spur rapid job growth. On Friday, four days before Election Day, the government is scheduled to issue the jobs report for October.

The AP survey collected the views of private, corporate and academic economists on a range of issues. Among their views:

•The U.S. economy and job creation will remain weak the rest of this year but should pick up slightly in 2013. The economy will expand at a 1.9 percent annual pace in the second half of 2012, little changed from the first half. Next year, they think growth should amount to 2.3 percent, enough to boost hiring slightly.

•Americans’ average pay will trail inflation over the next three years, as it has for the past three, a slight majority of the economists say. The tight job market means many employers feel little pressure to raise pay. And rising prices for food and gas could swell inflation and reduce purchasing power.

•Lack of customer demand is most responsible for weak U.S. job growth, slightly more than half the economists say. Fewer than half say a bigger factor is a shortage of skilled workers or employer uncertainty about future taxes or regulations.

• The $1 trillion-plus budget deficit isn’t significantly worsened by the nearly half of Americans who pay no income tax or by the lower effective rate paid by the top-earning 1 percent compared with a decade ago. Fewer than one in five of the economists think either factor is a major contributor to the deficit.

The economists also think the depth of Europe’s crisis has made Mario Draghi, president of the European Central Bank, even more crucial to the global economy than his counterpart in the U.S., Federal Reserve Chairman Ben Bernanke.

Europe is struggling to control a debt crisis, save the euro currency and prevent the entire region from slipping into recession. If its crisis spread to the United States, another U.S. recession would be possible.

Slightly more than half the economists surveyed by the AP say that for Europe, the worst is yet to come.

The economists continue to give high marks to Bernanke’s leadership of the Fed, which last month said it will buy $40 billion in mortgage bonds each month until the job market substantially improves.